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Department of Economics
2026-02-07
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Inline math: The treatment effect is \(\tau = E[Y_i(1) - Y_i(0)]\).
Display equations:
\[ \hat{\beta}_{OLS} = (X'X)^{-1}X'Y \]
Aligned equations:
\[ \begin{aligned} Y_i &= \alpha + \tau D_i + X_i'\beta + \varepsilon_i \\ E[\varepsilon_i \mid D_i, X_i] &= 0 \end{aligned} \]
Assumptions
These are necessary for causal identification under the DiD framework.
Diagnostics
Always validate assumptions before interpreting estimates.
| Estimator | Bias | Variance | MSE |
|---|---|---|---|
| OLS | Low | Low | Low |
| IV | None | High | Med |
| LASSO | Med | Low | Low |
| Matching | Low | Med | Med |
Key Result: Under parallel trends, the DiD estimator is unbiased for the ATT.
Highlight: This approach extends naturally to staggered adoption settings.
Method: Estimate using two-way fixed effects with clustered standard errors at the unit level.
Assumption (Parallel Trends): In the absence of treatment, the average outcomes for treated and control groups would have followed the same trend over time.
Result: The estimated ATT is 0.15 (SE = 0.04), statistically significant at the 1% level.
The credibility revolution in economics has shifted the focus from identifying assumptions to research designs that make those assumptions more plausible.
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